Study of the $D_s^{+}\to a_0(980)\rho$ and $a_0(980)\omega$ decays

Abstract

We study $D_s^{+}\to {\rho }^{0(+)}{a}_0^{+(0)}$, $D_s^{+}\to \omega a_0^{+}$, and the resonant $D_s^{+}\to \rho a_0$,$a_0\to \eta \pi (KK)$ decays. In the final state interaction, where $D_s^{+}\to ({\eta }^{(\prime )}{\pi }^{+},K^{+}{\bar{K}}^0)$ are followed by the $({\eta }^{(\prime )}{\pi }^{+},K^{+}{\bar{K}}^0)$ to ${\rho }^{0(+)}{a}_0^{+(0)}$ rescatterings, we predict $\mathcal{B}(D_s^{+}\to {\rho }^{0(+)}{a}_0^{+(0)})=(3.0\pm 0.3\pm 1.0)\times 10^{-3}$. Due to the cancellation of the rescattering effects and the suppressed short-distance $W$ annihilation contribution, we expect that $\mathcal{B}(D_s^{+}\to \omega a_0^{+})\simeq \mathcal{B}(D_s^{+}\to {\pi }^{+}{\pi }^0)<3.4\times 10^{-4}$. In our calculation, $\mathcal{B}(D_s^{+}\to {\rho }^0(a_0^{+}\to )\eta {\pi }^{+})=(1.6_{-0.3}^{+0.2}\pm 0.6)\times 10^{-3}$ agrees with the data, whereas $\mathcal{B}(D_s^{+}\to {\rho }^{+}(a_0^0\to )K^{+}{K}^{-})$ is 10 times smaller than the observation, which requires a careful examination.

Comments: 11 pages, 2 figures, version to appear in EPJC